I have noticed patterns among professors, who seem to follow mathematics so blindly (dangerously so, imo) that they fail to see the quick, intuitive shortcuts that I see. It's as if he doesn't "see" things with intuition, but rather relies on the crutch of mathematics, which does all the work for him. When, I ask him the answer to a certain problem, it's as if he says: "Hmm, well let's see what math says it should be.., because I don't have my own brain. Let me just take this variable called y, do something funny to it, and wallah, out comes the answer. I didn't figure that out for myself, mind you, I let math do the trick"
CyberShot wrote:I just have this deep-down gut feeling that any and everything in the world can be reduced to +,-,*,/ operations. I also feel like if we can reduce them to this basic, "proper" form, then we have truly conquered and understood the idea.
Captain_Slow wrote:Any good upper level physics book paired with a mathematical physics book (I like Hassani's) should give you a development of the methods, and the reason of usage of these "complicated" formulas.
CyberShot wrote:
I know for a fact that's the way the universe works. It's logical that it must work that way.
CyberShot wrote:They'd rather invent complicated looking formulas (like tensors) that boost their ego, so as to exclude others and make themselves feel like they are the best and brightest.
meichenl wrote:I have noticed patterns among professors, who seem to follow mathematics so blindly (dangerously so, imo) that they fail to see the quick, intuitive shortcuts that I see. It's as if he doesn't "see" things with intuition, but rather relies on the crutch of mathematics, which does all the work for him. When, I ask him the answer to a certain problem, it's as if he says: "Hmm, well let's see what math says it should be.., because I don't have my own brain. Let me just take this variable called y, do something funny to it, and wallah, out comes the answer. I didn't figure that out for myself, mind you, I let math do the trick"
I also like intuitive explanations where they're possible, but ultimately a reasonable balance in necessary. Also, what is considered "intuitive" depends on the person. I do not consider it mysterious that the integral of x^n is 1/(n+1) x^(n+1) or consider it a trick. I think the concept of using antiderivatives to compute integrals is very intuitive, and further that it's intuitively pretty obvious that the derivative of x^(n+1) scales as x^n by simple dimensionality. The exact coefficient isn't obvious to me, (except for small n, where I can visualize an n-dimensional box expanding) but the rest is not so bad.
I'm reminded of an essay by John Baez, "Mysteries of the Gravitational Two-Body Problem" (http://math.ucr.edu/home/baez/gravitational.html) that addresses this issue. Baez says that in his whole career as a mathematical physicist, despite seeing many mathematical proofs that orbits in a 1/r^2 force law are conic sections, "I'm still looking for the truly beautiful way, where you leave the room saying: 'Inverse square force law... conic sections... of course! Now the connection is obvious!'".
The lesson is threefold. First is that many other people are interested in understanding things as intuitively as possible. Second is that this is not always possible, or at least not always easy. The final one is that this doesn't mean physics is in error or ugly or not working. It just means that the consequences of the laws aren't obvious. Doesn't that add to how remarkable they are? Isn't it fantastic that the universe computes such rich, wild, unintuitive results all the time?
I don't know about your professors, and mine varied in quality during lectures, but on the whole they were outstanding. I had the privilege of auditing the last course Kip Thorne taught before retiring - a survey of classical physics including relativity, statistical mechanics, and continuum mechanics. He had an incredible ability to meld both intuitive and mathematical understanding, and he mixed this with stories about the times in his career he had applied this knowledge (sometimes to LIGO, and other times to things like building his house to withstand windstorms), videos of the motion we were analyzing, and historical context to the problems we were solving. In fact I deeply regret lacking the discipline to keep up with the reading and homework outside of class to absorb as much as I could from the experience. (The lecture notes, which are really a fully-formed book, are available at http://www.pma.caltech.edu/Courses/ph136/yr2008/
You might also be interested in things like Sanjoy Mahajan's book on intuitive mathematics http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=12156 (free download available) or his notes on order-of-magnitude physics http://www.inference.phy.cam.ac.uk/sanjoy/oom/, or Sterl Phinney's class on the same topic http://www.its.caltech.edu/~oom/. Here, the goal is to take physics phenomena and get rough intuitive understanding without much mathematical manipulation. In some cases it's amazingly powerful.
Finally, you might enjoy Mark Levi's book "The Mathematical Mechanic", which turns the picture on its head, using intuitive physics concepts to understand mathematical ideas!
CyberShot wrote:It's as if calculus, or any other invented math is like a language, which gets converted into binary (the mathematical equivalent of + - * /) so that it can be implemented to spit out an answer.
The_Duck wrote:Anyway, multiplication just stands for repeated addition, and division [in a way] for repeated subtraction, and subtraction for addition of a negative number, so just stick with +.
CyberShot wrote:I guess I can make a computing analogy here.
It's as if calculus, or any other invented math is like a language, which gets converted into binary (the mathematical equivalent of + - * /) so that it can be implemented to spit out an answer.
In this way, we should be able to figure out any problem we want by just adding, subtracting, multiplying, or dividing quantities. These 4 concepts are built into the universe (the rest are man-made) and that's the level at which I want to understand physics.
ZapperZ wrote:Maybe what you actually love is NOT physics, but rather the romanticized view of it.
I will also point out that what you call "intuition" is nothing more than a series of knowledge that you've acquired till now. I can show you many situations where your intuition will fail, simply because you haven't been exposed to that particular knowledge. And when you have, then you find that to be intuitively obvious. So relying on your intuition is not reliable, especially when you're still learning and when you don't know a lot.
Zz.
ZapperZ wrote:
To me, that is more frustrating than learning mathematics. And considering that philosophy doesn't play a role at all in the advancement of physics, but rather having to play catch-up with the new things in physics, you have to be consider if what you do makes any difference.
micromass wrote:Yes, I agree. I don't really like philosophy to for that very reason. But I simply think that the OP might be more philosophy minded. And I think that the OP should do what he loves best, and in this case I don't think physics is really his thing.
I mean, if you're loving the concept of time travel, then I think philosphy is the field where you can talk about that concept freely. It's not science at all, but I simply think that the OP might like philosophy more then the hard, cold sciences...
JDStupi wrote: Oh yea, and let's not be so sure about philosophy being the easy-breezy place where we can freely speculate on anything we wish. Maybe you should take a philo course, and maybe you'd end up right back where you started. A good Philo course wouldn't stand up for
"These 4 concepts are built into the universe (the rest are man-made) and that's the level at which I want to understand physics"
What is your justification for this statement? Where did you get this idea from? How do you proceed from a personal familiarity to an ontological statement? Assuming you could logically prove that all mathematical operations were reducible to elementary arithmetic operations, how would you proceed from a statement of mathematics/logic to a statement of ontology/metaphysics? ....
Fizex wrote:
I'd like to see how you can put 5^pi in terms of those operations without infinitely approximating.
Fizex wrote:
Have you taken quantum mechanics yet? No human intuition is going to let you derive the solutions to it's problems.
CyberShot wrote:1. If every physics problem can possibly be done by adding, subtracting, multiplying, or dividing a bunch of numbers, then these 4 concepts underpin reality in some way.
2. Every physics problem can possibly be done by adding, subtracting, multiplying, or diving a bunch of numbers. *
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3. Thus, these 4 concepts underpin reality in some way.
CyberShot wrote:2. Every physics problem can possibly be done by adding, subtracting, multiplying, or diving a bunch of numbers. *
CyberShot wrote:Things requiring an infinite amount of time does not place them outside the realm of "possibility."
CyberShot wrote:I actually believe that intuition is not learned, but rather pre-programmed into our brains before birth. I'm sure you're familiar with Molyneaux's problem.
CyberShot wrote:A bit harsh, and (no disrespect) miscalculated response, don't you think? Philosophy makes statements about why physics and math are the way they are, or why they're even allowed to work in the first place. It's sort of like the pre-heat part of the instructions in making the universe. Sure, some philosophical statements can probably never be proven, but that's why we're granted some intuition to see if such statements are plausible.
CyberShot wrote:Simple argument, see if you can break it.
1. If every physics problem can possibly be done by adding, subtracting, multiplying, or dividing a bunch of numbers, then these 4 concepts underpin reality in some way.
2. Every physics problem can possibly be done by adding, subtracting, multiplying, or diving a bunch of numbers. *
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3. Thus, these 4 concepts underpin reality in some way.
Argument 1 presupposes a connection between mathematical truths and metaphysical ones, a not so improbable one if you deeply think about it.
It might be hard to see 2 right away. To convince yourself, try to think of a counter-example. Granted, to do calculations using the 4 basic operators might take an infinite amount of time to do so, and it may also be infinitely tedious, but it's definitely possible. Things requiring an infinite amount of time does not place them outside the realm of "possibility." Neither does tediousness.
CyberShot wrote:Exactly why it's probably a stubbornly wrong model of reality, not that I'm qualified (as in a physics degree) to make such statements about ludicrous theories that include two particles deciding on their own accord to "communicate" with each other without actually communicating.
CyberShot wrote: I just have this deep-down gut feeling that any and everything in the world can be reduced to +,-,*,/ operations.
Ryalnos wrote:As drunkenscientist (sorta) pointed out with his link, believing so strongly that you are thinking about the world correctly and (almost) everyone else is wrong is a bad sign/the road to becoming a crackpot.
CyberShot wrote:1. If every physics problem can possibly be done by adding, subtracting, multiplying, or dividing a bunch of numbers, then these 4 concepts underpin reality in some way.
2. Every physics problem can possibly be done by adding, subtracting, multiplying, or diving a bunch of numbers. *
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3. Thus, these 4 concepts underpin reality in some way.
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